UKC

Assuming an ideal surface and the ideal choice of angle (for each), would a top cyclist gain height quicker than a top runner, or the other way around?

And would the same be true for descending?

youtube.com/watch?v=RFwrGa6IswY&

I'm voting downhill for the bike.

45 degree slope and a max speed of 167.6 km/h (104.1 mph).

Ascent. On a slope of more than 20% I reckon the runner has it as well.

Common sense would say that the weight of the bike would count against the cyclist in ascent, the runner would have no chance against the bike in descent. Killian's 1km FKT is under 29 minutes up, assume he would be quicker down, but surely a determined mountain bike rider would beat him? Interesting question..

Depends on what distance and under what conditions, but not a lot in it. Long distance (>100m gain) I think the cyclist would in practice win: slight efficiency advantage but extra weight of bike. Short distance and standing start I would favour the runner. Guess work.

Cyclist much faster as long as you don't count 'falling'. The runner is very limited by leg speed/strength. The cyclist is just limited by aerodynamics. And balls.

The counter argument would be that cycling is an inherently more efficient action than running. I'm pretty sure that over a short distance, a runner could gain height quicker than a cyclist, but I'm less sure that this would hold true over longer distances.

I assumed it was 'ideal for each'. Having said that on a bike the max height gain is on the max slope given the bike's gearing (minimises aero  and RR losses) and the cyclist can choose whatever gearing will allow him/her to do 80rpm (typ max power) up whatever slope. The limiting slope will be determined by traction and will be >20% on decent tarmac.

Runner, if it's steep enough that the biker is down in the granny gears grinding away. 

Define long, it's kind of what we evolved to do, wear down our prey over long distances, where we are quite efficient, can dissipate heat etc. Man versus horse run being a classic. Obviously a bike is person v person, but i think a few similar principles still apply. 

Good question.

Ideal surface would assume smooth slope for both at first, but a runner at steeper angles would possibly favour steps.

For the same height gain, I'd expect results will vary according to steepness - lower angles will favour the bike, steeper angles will favour the runner. Past a certain point, it will be impossible to ride the bike and keep the front wheel down.

You can get the bike weight down to sub-5kg, I think, if you strip it down to bare essentials, so wouldn't expect that to influence results that much, given the efficiency gains.

Downhill, I'd be betting on the bike every time!

According to this calculator https://www.gribble.org/cycling/power_v_speed.html?units=metric&rp_wr=7... a cyclist only needs to do 438W to get up a km in Killian's time, which is not really that high (for a top pro).

The fastest running ascent of the last 10km of the Tourmalet is a professional runner in 53:30 (12kph)

The fastest bike ascent of the same is a professional cyclist in about half an hour (there isn't an exactly corresponding Strava segment) at 20kph

That was also the second of three climbs on day 6 of the Tour de France, whereas the runner set out specifically to do the Tourmalet.

I know I've definitely been overtaken by runners while on a mountain bike, uphill on a gravel track. 

But in ideal conditions, I'm not sure but it would be fun to find out. Perhaps ascending stairs would be optimum for a runner? See how long it takes an elite athlete to ascend say 100m in a tall building then compare it to a top cyclist times up various passes for a 100m worth of climbing. 

Why similar principles for man vs. man compared to man vs. horse? Doesn't make sense. I think the key differentiator between running and cycling physiology is the power distribution over one cycle (step or crank rotation). My gut feeling is that running will involve much more acceleration/deceleration (per leg cycle) than turning a crank, so will be less efficient. The Killian example above supports this. Bearing mind that John's original question specified that the runner and the cycling each get to choose their own optimal slope/surface.

Yes, based on my own feeble efforts on a road bike, I reckon at 20% I'd be quicker getting off and 'running'.

As another 'real world' data point, the everesting* record on a bike is 6h50 and for running its 8h52.

Although that includes any descents, so favours the cyclist (perhaps).

* https://everesting.cc/

I think a lot of people are missing the phrase "ideal for each" here - AIUI the idea is that you've got a height gain of 300 metres (say) to the top of the pass, but the bike can get there via one road - presumably fairly gently angled and meandering - while the runner can take a steepish road or a super-steep stepped path or whatever suits them.

No idea what the answer is, though.

If they're going their own optimal ways then the cyclist. Much more efficient, they're sitting down!

Bingley's annual Harriers v Cyclists race is a great mixed test and surprisingly close between runners and riders. The winner often depends on the amount of mud on the descent from Baildon Moor.

I've done it both as a runner and a rider and can confirm that I'm much quicker running due to a complete lack of confidence and technical ability on a bike.

https://www.webscorer.com/race?raceid=336349

I have a strava segment, running, of 128m of ascent in 2 minutes and 50 seconds. That is 45 metres per minute of ascent which is a good bit faster than the quoted Tourmalet times below. The last 10km of the Tourmalet has between 800 and 900m of ascent, in half an hour that would be between 26 and 30 metres per minute of ascent and that is for pro cyclists. When I ran that time I was an office worker who hadn't ran competitively for over 10 years with recurring injuries meaning that I barely ran at all (but was fairly active). The route in question was mostly comprised of very steep rocky steps and some tarmac for the first not so steep bit, total length 540m. Get an actual in form athlete on it and they should be able to beat my time (currently the only person ahead of me has recorded it in 1:01 which I don't believe). Therefore, while the cyclists can generate a higher power output argument is alluring I think the fact that runners can go up much steeper hills than cyclists allows them to post higher m/minute vertical times

An actual athlete:

https://www.strava.com/segments/8079807

63 meters vertical per minute over a 675m climb. I would be shocked if any cyclist could come close to that

oops, that's the descent!

https://www.researchgate.net/publication/257820274_Engine_Matters_A_First_L...

Record Tour de France climbing rate is approx 1865m per hour, Contador on the Verbier climb in 2009, that is 31m per minute. Easy win for runners

For a cyclist going steeply uphill (20%) pretty much all the power (90%+) goes simply into lifting his weight against gravity. The horizontal component (aero, RR) is largely irrelevant.

Line graph. Speed against incline, plot a line each for the cyclist and runner, they'll be different, but at a given point they'll intersect where the runner becomes the faster.

There are efficiencies in cycling, but so too in running. Once a cyclist has hit bottom gear, there's no where else to go, the same with runners altering stride length and cadence, it's a question of the angle required. 

Principles, horses have different advantages for endurance just like bikes, but once a horse is walking, it's like the bike in lowest gear. 

at 30kph, that 31m ascent could be over 500m. That's some running speed. Did you see how fast Pogacar did the last 5km up hill the other day? I think it needs to be much steeper for a running win. 

I don't think John's envisioning the runner and cyclist using the same course. Each competitor gets their own ideal terrain.

If it's purely a height race, then the runner still probably wins. There's a race up the empire state stairs, 300m, 11 minutes and a bit is the record.

Yes, I tried to make that clear in the OP. From several responses it seems I wasn't as successful as I'd hoped.

Let me rephrase.

How would the maximum rate of height gain of a top runner, given a choice of angle, terrain and surface, compare with the maximum rate of height gain of a top cyclist, given their own (almost certainly different) angle, terrain and surface preference?

Pogacar at 600W will do that in just over 7mins on a 25% slope. No contest.

I'm not sure the stairs of a skyscraper are the optimum for the runner anyway though. Not least because of all the turns. But also because the steps force a very specific stride pattern that's unlikely to perfectly suit anyone and doesn't allow many options to vary the stride as they fatigue.

Trying to find a record hill time, harder than I thought, as races always involve the descent as well. 

There is the option of a little arm assistance from the handrails, mind...

I think the Empire State must be tricky to negotiate, because that sounds pretty slow. I did 22 Bishopsgate (about 260m to the 59th floor) in 13 minutes without trying hard, and I'm no athlete (25mins for a 5k).

True, but a recent data point is yesterday's stage where TP went up to the Plateau de Beille (15.8km @ 7.9%) in 39mins. That's a 1.25km vertical ascent. The slope isn't really steep enough - he's wasting about 100W just on aero and rolling resistance losses. And that's at the end of a 4h hour race with 4000m of climb in the bag already in 30+C heat. So even with all that he's ascending significantly faster than your Empire State runner already.

Yes - I'd implied, but not explicitly stated that.

For "ideal", I'd assumed 2 separate start points at the same altitude with the same finish - the runner with a short and steep climb, the cyclist with a longer, but shallower climb.

Both routes would need to be straight, for fairness - no switchbacks for the cyclist.

I'm guessing there's a sweet spot somewhere with the same time for both.

IMHO the runner is only going to win once the slope gets high enough that the bike loses traction and become unridable.

My own experience (definitely not a top runner or cyclist!) is that for the same perceived level of effort, my rate of ascent is about the same on the bike or on foot.

My guess is that the same will hold true for top runners and cyclists too. At slow speeds over the ground, both are working mainly against gravity.  The cyclist perhaps benefits somewhat from being able to remain seated, but also has to carry an extra 10% of weight up the hill.  

The answer is a UKC classic - treadmills!

Which is faster climbing on an inclined treadmill in a window tunnel to match gradient and air resistance?

I have read a study (will link it if I can find it) From memory it was between 15-20% on a road bike/tarmac and 9-12% on a mountain bike/off road.

It doesn't really answer the OP as this was recreational/club athletes comparing their own times up real hills. So not elite athletes or ideal conditions

I think I'll have to find some hills and test myself. I'm curious now, it's just finding that right gradient for a reasonable distance. Obviously us mortals might differ to Pogacar or Finlay Wild going up hill. 

Just need the OP to pin down the test parameters: Peak speed or averaged over some defined distance/time? Standing start or rolling start? How many reps (affects both error analysis and pacing)?

On a turntable...

But the Tourmalet isn't 20% + is it?

Some 15 years ago I bet my 13yr old (£15) that I could run up snowdon and back from Llanberis faster than he could cycle the same route. I got to the top way before he did and to the half way house on the way down before I was resoundly passed by a screaming teenager going at ramming speed. We did the bet way before the hoards and afterwards enquired why was he going so bloody fast? His brakes had worn out…

Seems it might depend on how many kebabs the cyclist's eaten: https://road.cc/content/news/cycling-live-blog-16-july-2024-309441#live-blo...

I have now spent too long looking at this question and I still believe that runners can maintain a higher VAM (vertical ascent in meters per hour) than cyclists but that it is a lot closer than I originally thought. I based my initial assessment on that fact that  have a 128m climb on strava (running) with a VAM of 2790 m/hour and no cycling stretch that I can see comes close. On closer inspection though that climb is probably 90 - 95m which would reduce my VAM to between 1900 - 2000 m/hr (possibly still unrealistically high, long before I recorded that I was a good but not exceptional full runner, although I did go all out on that climb).

Bamford Clough makes an interesting comparison, one of the steepest sustained roads in the UK with identical running and cycling sections on Strava, but almost certainly gets more attention from serious cyclists than runners (runners have enough off road climbs to get stuck into that it doeesn't have quite the same level of importance to them). Top cyclist time is 4:18, (VAM of 1963) top runner is 4:22 which would place him place him 2nd on the cyclist leaderboard so essentially neck and neck (the VAM figures don't quite tally, limitations of Strava are more apparent for heights)

https://www.strava.com/segments/29879743

https://www.strava.com/segments/2501770?hl=en-GB

GCN reckon that Scanuppia is the steepest road in Europe and their man Andrew Feather has the win on it with a VAM of 1515 m/hr. This might suggest that when it is too steep for the bike to be an effective tool but it is also about 3x as long a climb as Bamford Clough which will explain a lot, if not all, in the reduction in VAM.

If you look at Kilian Jornet's strava profile, on the first page of CRs, he has has VAM that works out at 2213 m/hr for a section with more height gain than Scanuppia

https://www.strava.com/segments/20553255

If you flick he has loads more sections that equate to a VAM of 2000 or higher, and I can't find any cyling section with a VAM that reaches 2000. British hill climbing wins (cycling) work out at about 1960.

I think that this makes sense, its close but running has the edge likely as your arms are more useful than when cycling and you don't have the added mass of the bike. Your legs are doing are very similar action for running steep uphill versus cycling so its not that obvious that a cyclist can even output more power than a runner on the steeps.

There are obviously some big limitations in these comparisons, the athletes selected are not all directly comparable and Strava has clear inaccuracies with altitudes which can greatly affect the resulting VAMs. However, even correcting the heights for a Strava section gives me, an occasional/historical runner who cycle commutes (no actual training) about 3x a week a running VAM comparable with the best British cycling hill climbers when clearly my fitness is nowhere near theirs.

Next time I am in the Peak District I may have to have a crack at Bamford Clough, both on foot and on a bike, might make me re-evaluate my earlier claims and conclusions

VAM is definitely the way to look at this. 

Shame the vertical kilometre doesn't seem to be a 'thing' in cycling or this would be a really easy question to answer.

VAM calculation: VAM = (metres ascended × 60) / minutes it took to ascend. Units are metres per hour (m/h).

Kilian has the FKT for the vertical kilometre in running, 28:48 on a route he specifically selected to be optimal for getting the FKT, with specific preparation/training for doing so and multiple attempts. https://en.wikipedia.org/wiki/Vertical_kilometer

Kilian's vertical km FKT VAM = 1000*60/28.8 = 2083 m/h, sustained for 0.48 hours.

A couple of days ago on Plateau de Beille (15.7km, 7.8%), Pogacar did 15700*0.078 = 1225m of ascent in 39:50, said to be the greatest cycling climbing performance ever in terms of watts per kilogram (W/kg). https://lanternerouge.com/2024/07/14/greatest-climbing-performances-of-all-... This was into a headwind, but also he was in the draft for the majority of the climb. It had been an incredibly hard stage beforehand. 7.8% is definitely not the optimal gradient for maximising VAM, not steep enough.

Pogacar Plateau de Beille VAM = 1225*60/39.83 = 1845 m/h, sustained for 0.66 hours.
(Actually reported here https://x.com/WattsinCycling/status/1812516460578639997 as a VAM of 1887 m/h).

If Pogacar or Vingegaard had a go at the vertical km (assuming a suitable road exists) I reckon they'd be faster than Kilian.

Loving the TLA, I'm off out VAM training later, might even blog about it on my non existent instatok account as some new training concept, that will push your FTP to new levels! 

The 2022 champs up to the Ponderosa Cafe had the top 10 under 6 minutes. I'm always wary of the accuracy of shorter segments but strava has it's height gain of 213m. Feathers wining time of 5:17 must have a VAM of well over 2000 and that is on a gentle hill of under 14%.

Hmm. Pogacar sustained 1920m/hr for 39min at the end of a fairly hectic 4h stage with >4000m of climbing. I'm pretty sure he'd go significantly over 2000m/hr in a one-off time trial. If he was bothered. 

On something like the Bamford climb (30%?) you only need ~470W to reach 2000m/hr. On something that short (<500m) I'd expect a top pro to do 700-1000W which equates (roughly) to 3-4000m/hr.

Still, I'm glad someone is taking this problem seriously!

There is a hill in Norway

https://climbfinder.com/en/climbs/lysebotn

Which has several different races up it, roller ski, run, bike etc.. sadly they don't all use the same courses or distance. Even on strava the segments differ, so hard to compare. Bikes appear the winner though, I just don't think it's steep enough to give runners a look in(it is also driveable), they still average quite a good rolling speed. The bike course is longer as it levels out and overall they average 30kph, runners 5min/km on the steeper bit. So hard to calculate VAM individually, but even when steep the cyclists won't be dropping to 12kph. 

Note: Andrew Musgrave the uk's best nordic skier (probably ever) has won the roller ski event and placed well a few times. 

Andrew Feather averaged 22.5km/h up the Struggle at the National Hill Climb last year, nobody is running up there that fast!

This must be fairly easy to consider from a physics stand point no?

Pro cyclists will pump out about 5W per kg on sustained climbs like alp d'Huez.

So if a runner can't match that power output then (theoretically) the cyclist wins.

What we need though is some data on power output v.s. gradient for both running and cycling.

Though, if we allow the cyclist to gear the bike appropriately such that the 'effective gradient' is the optimum for max power output the cyclist always must win right? Like it could be up the side of a cliff and if the cyclist had magic sticky wheels and a low enough gear ratio they'll be much faster than someone trying to run up the cliff, even if they have magic anti-gravity shoes. 

So it basically boils down to who can convert the most energy from their muscles into potential energy and the cyclist is always going to be more efficient right?

​​I think that's logically sound!

No not really. Yes, the physics (lifting mass against gravity) is simple, but the human physiology (power output when cycling/running) isn't.

Yep, that's the hard bit! Like you I *think* cycling is more efficient, but it's hard to prove. And it needs enough margin to overcome the added mass of the bike.

Just proves that logic only gets you so far.

It boils down to whether cycling can be a more effective harnessing of muscle power than running, so as to generate a higher effective power output, and enough of an advantage to compensate for having also to move the weight of the bike up too. I don't think the answer is at all obvious, assuming we're not trying to force both to use the same gradient.

A couple of bonus questions:

Could any MTB cyclist beat Kenny Stuart's Snowdon record (up and down in 1:02:29)?

How much quicker is a speed climber than either runner or cyclist (admittedly over a much shorter distance)?

Quicker, but it's probably a unfair comparison since speed climbing is essentially an anaerobic activity (more akin to high-jump) whereas most running/cycling is aerobic. Completely different physiological energy mechanisms at play.

Anyway, you still haven't defined the distance/time for the running/cycling showdown

I haven't defined it because I'd like to know if the distance would change the outcome!

In terms of aerobic/anaerobic, there are sprint disciplines in both running and cycling too, which could properly be compared with speed climbing.

Probably a second order effect. I have a feeling that any definitive answers will elude us. Nice sports science problem for some students perhaps? Or perhaps you should sponsor the Arran Prize for the fastest vertical kilometre by runner/cyclist? 

Not many that are over in less than 5s!

I've seen figures of 25-27W/kg for track sprinters, how long are they maintaining that for? 

If I had money to do so, that sounds like it would be a cool use of it!

Good point. Uphill sprinting isn't really a thing either, as far as I'm aware, in either running or cycling, other than in terms of hill training. I've never heard of a race that takes less than 30 seconds.

Upthread Kilian Jornet is quoted as managing a VOM of 2083m/hr for just shy of half an hour, on actual mountain. The following link reckons that a rider finishing in the top 10% of the TdF could manage 6.24W/kg over half an hour. Assume a 66kg rider + an 8kg bike (the mass would cancel out apart from the mass of the bike stays the same) and 100% efficiency amd that would give a VOM of 2042m/hr, just shy of Jornet's actual pace. Throw in a 10% loss due to rolling resistance, drag, and drivetrain resistance and then Jornet takes the win by 10%. 

https://www.wattkg.com/power-records/

If Jornet's fitness (measured in Watts/kg over 30 minutes) is comparable to a top 10% TdF rider then this suggests that running is the faster way to gain height, if his fitness is lower then it gives running an easy win, and if his fitness is higher then it might give cycling the win

I think it might come down to the length of the effort. If we are talking about ascending a relatively short vertical distance - say 1000m or less - then running will win because of its greater power. But the increase in efficiency of cycling might win out on longer efforts (over 1000m height gain). Obviously all guesswork…

My only direct comparison is on a hill behind my work. It’s 800m long, tarmac, 80m height gain. I’ve run it in 3.40; on a bike I’ve done 2.50, also full gas. So, a lot quicker than running but that’s mostly because of the relatively flat run-in. I reckon on the steep top bit there is very little in it. A very strong cyclist could do the full hill in under 2 minutes; a world class runner could probably do similar.

Downhill I’m not sure. Road riding gets to incredible speeds but rarely dropping height that quick, maybe 1000m in 12 minutes is about the limit. I reckon that’s doable for runners. How fast is a quick time down Aonach Mor for an MTB?

A steep stair case is going to be 45 degrees so a 100% gradient not 25%

Well if it's tricky to negotiate for a runner try and picture doing on a bike!

It's not really a mystery  is it. If you watch the Tour or Vuelta you see the top riders on steep hills being cheered on by spectators who run along side them keeping up without any trouble. These are not fit runners trying to out pace them.. I've also seen riders dismount and go faster in cleated cycling shoes than they were going on the bike. Basically at a certain steepness the bike is a disadvantage.

Danny MacAskill's next project? Although you don't see him going uphill that much.

I've seen him going up a pretty reasonable hill once. Admittedly he was carrying the bike though.

I bet those runners haven't run the previous 200km? Or even from the bottom. 

Has anyone ever ran Ventoux 3 times (cinglés)?

The OP asked us to compare running and cycling under ideal conditions for each - which could include, say, a steeper angle for runners.  My own experience is that I can walk up a far steeper angle than I can ride a bike.  I achieve about the same vertical rate of ascent on foot as on the bike, when going full steam ahead.

I've had to dismount, on very steep slopes, on a mountain bike, because I was barely doing walking pace but using more energy, than walking, to achieve it.

Some relevant recent head to heads:  youtube.com/watch?v=To0VBPo4GQs&